Relativistic calculations of quasi-one-electron atoms and ions using Laguerre and Slater spinors

Abstract

A relativistic description of the structure of heavy alkali atoms and alkali-like ions using S-spinors and L-spinors has been developed. The core wavefunction is defined by a Dirac-Fock calculation using an S-spinors basis. The S-spinor basis is then supplemented by a large set of L-spinors for the calculation of the valence wavefunction in a frozen-core model. The numerical stability of the L-spinor approach is demonstrated by computing the energies and decay rates of several low-lying hydrogen eigenstates, along with the polarizabilities of a $Z=60$ hydrogenic ion. The approach is then applied to calculate the dynamic polarizabilities of the $5s$, $4d$ and $5p$ states of Sr${}^{+}$. The magic wavelengths at which the Stark shifts between different pairs of transitions are zero are computed. Determination of the magic wavelengths for the $5s\to 4d_{\frac{3}{2}}$ and $5s\to 4d_{\frac{5}{2}}$ transitions near $417$~nm (near the wavelength for the $5s\to 5p_j$ transitions) would allow a determination of the oscillator strength ratio for the $5s\to 5p_{\frac{1}{2}}$ and $5s\to 5p_{\frac{3}{2}}$ transitions.

2 figures, 23 pages

References in corpus (9)

• CODATA Recommended Values of the Fundamental Physical Constants: 2014
• Relativistic coupled-cluster single-double method applied to alkali-metal atoms
• Measurement of magic wavelengths for the 40Ca+ clock transition
• Magic wavelengths in the alkaline earth ions
• Accurate solution of the Dirac equation on Lagrange meshes
• Relativistic polarizabilities with the Lagrange-mesh method
• Ab initio determination of polarizabilities and van der Waals coefficients of Li atoms using the relativistic CCSD(T) method
• Polarizabilities of the Mg${}^{+}$ and Si${}^{3+}$ ions
• Static electric multipole susceptibilities of the relativistic hydrogen-like atom in the ground state: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function

Cited by in corpus (8)

• AMBiT: A program for high-precision relativistic atomic structure calculations
• Electric dipole transition amplitudes for atoms and ions with one valence electron
• Angle-dependent magic wavelengths for the $4s_{1/2}\to 3d_{5/2,3/2}$ transitions of Ca${}^{+}$ ions
• Combination of the Perturbation Theory with Configuration Interaction Method
• Magic wavelengths for the $6s^2{}^1{S}_0-6s6p{}^3{P}_1^o$ transition in ytterbium atom
• Magic intensity trapping of the Mg lattice clock with light shift suppressed below $10^{-19}$
• Relativistic semiempirical-core-potential calculations in Ca${}^{+}$, Sr${}^{+}$, and Ba${}^{+}$ ions on Lagrange meshes
• Relativistic hyperpolarizabilities for atomic H, Li, and Be${}^{+}$ systems